Average Score Difference Calculation

This solution details the process of finding the average score difference for player A across nine games, using the provided results of games won and lost.

Analyzing Game Results

Here's a breakdown of the information provided:

• Total games played: 9
• Games won: 5 with score differences of 12, 3, 8, 4, and 1.
• Games lost: 4 with score differences of -4, -1, -2, and -3.

Calculating Total Score Difference

To find the average, we first sum the score differences from all nine games.

Step 1: Sum the score differences from the games A won.

Sum of differences in won games = $12 + 3 + 8 + 4 + 1 = 28$

Step 2: Sum the score differences from the games A lost.

Sum of differences in lost games = $(-4) + (-1) + (-2) + (-3) = -10$

Step 3: Combine the sums to find the total score difference across all nine games.

Total score difference = (Sum of won game differences) + (Sum of lost game differences)

Total score difference = $28 + (-10) = 18$

Determining the Average Score Difference

The average score difference is obtained by dividing the total score difference by the total number of games played.

Average Formula:

$$ \text{Average Score Difference} = \frac{\text{Total Score Difference}}{\text{Total Number of Games}} $$

Applying the values:

Average Score Difference = $ \frac{18}{9} $

Average Score Difference = $ 2 $

Conclusion

The average score difference for player A across the nine games is 2.